The Doctor's regeneration has left him mentally unstable. He changes his cricket attire for an outfit of clashing colours, including a multicoloured patchwork frock coat. After almost killing Peri during a fit of instability he decides to live as a hermit to avoid putting others at risk.

On Earth, mathematical genius twin brothers Romulus (Paul Conrad) and Remus (Andrew Conrad) are kidnapped by Professor Edgeworth (Maurice Denham). The kidnapping is discovered – tell-tale traces of a material called zanium are found on the floor – and a squadron of space fighters under the command of Lieutenant Hugo Lang (Kevin McNally) is sent to pursue the X.V.773 Space Hopper Mk III Freighter on which Edgeworth is escaping with the twins. The fighters are attacked, leaving Lang as the sole survivor when his ship crashes on the asteroid Titan 3. The TARDIS lands here too, and the Doctor and Peri find Lang in the wreckage. The Doctor reluctantly agrees to investigate a distant dome, which is in fact where Edgeworth has taken the twins as a halfway safe house on his journey back to the planet Joconda. 

The Doctor and Peri arrive at the dome only to be captured by Edgeworth's two Jocondan guards, Noma (Barry Stanton) and Drak (Oliver Smith). Edgeworth is recognised by the Doctor as a retired Time Lord whose real name is Azmael. Azmael had ruled Joconda since his retirement, but the planet has now fallen under the control of a race of giant Gastropods – slug-like creatures from Jocondan mythology – led by Mestor (Edwin Richfield), who is now forcing Azmael to do his bidding. 

The Doctor and Peri are left sealed in the dome as Azmael and the others leave for Joconda. When they are alone, they discover that the dome has been set to self-destruct – an action taken by Noma without Azmael's knowledge. The Doctor hastily adapts a Revitalising Modulator to transmit his and Peri's molecules back in time to the TARDIS and thus escape the destruction of the dome. To his amazement, it works. 

Together with Lang, who had been left behind in the TARDIS to recuperate while they explored the asteroid, the Doctor and Peri journey to Joconda, where they are soon captured and imprisoned with Azmael. Mestor claims to need the twins' mathematical prowess to provide the energy equations required to realise his plan of placing the Jocondan sun's outer two planets into orbit around Joconda, thus providing a ready-made larder facility. To balance the gravitational forces, Mestor wants all three planets to occupy the same space, but in different time periods, one Jocondan day apart. The Doctor realises that as the outer planets are small, the gravitational differences will pull them into the sun and cause a massive explosion. This is Mestor's real plan, as the explosion will activate millions of his eggs and send them out into space to fall on to other worlds, thus populating the whole of space with the giant slugs. 

The Doctor tries to destroy Mestor by throwing at him a vial of corrosive chemicals from Azmael's laboratory, but the attempt is thwarted when the creature raises a force shield around itself. Mestor now wants to possess the Doctor's body, and to prove that he is capable of doing so he attempts to mind-link with Azmael. While Mestor is distracted, the Doctor hurls a second vial of chemicals at him, and this time strikes the target. Azmael triggers his thirteenth and last regeneration, and Mestor's mind, having nowhere to flee now that his body has been destroyed, dissipates into nothingness. Unfortunately Azmael dies too. The threat from the Gastropods is lifted and the Doctor prepares to return the twins to Earth. Hugo elects to stay on Joconda to help the Jocondans rebuild their planet.

_{Synopsis from Doctor Who: The Sixth Doctor Handbook by David J. Howe, Mark Stammers and Stephen James Walker, reprinted with permission; further reproduction is not permitted. Available from Telos}